BAX/) WIDTH AXD TRAXSM/SSIOX PERFORMANCE 573 



Instead, a special kind of impairment is incurred at the terminals, because of 

 the fact that the speech wave is transmitted by quantized amplitude samples 

 of the wave. Transmitting; samples of a wave results in a received wave 

 ha\dng no impairment, provided the samples are not subjected to time or 

 amplitude distortion. In PCM, since the samples are telegraphed, their 

 reception is inaccurate by the quantization imposed by the code. These 

 errors in the samples constitute the sole inherent imj)airment in transmission. 



Strictly speaking, the transmission imj^airment in PCM is manifested only 

 when a signal is being transmitted. An imaginary telephone circuit with the 

 transmitting side completely devoid of any kind of signal, except that from 

 tl:e talker, could be transmitted by PCM from coast to coast and would 

 sound completely silent if the talker were silent. In any real situation, 

 however, some background noise (room noise, breath noise or line noise) is 

 always present in the subscriber's circuit. This background noise is usually 

 comparable to or greater than the weak parts of weak speech. In order to 

 transmit the speech of weak talkers the size of the discrete amphtude steps 

 must be small with the result that at least a few steps are always brought into 

 play by background noise. 



Being thus enabled to rule out the case of no signal we are able to ascribe a 

 basic signal impairment to a PCM system. This impairment is, strictly 

 speaking, a result of non-linear distortion inherent in the quantizing, but 

 because of its very complex nature it behaves, and sounds, much like thermal 

 noise and we have accordingly called it quantizing noise. A PCM circuit 

 can be regarded as a source of noise whose rms value is simply related to the 

 size of the quantizing step and the sampling frequency, as follows: 



In a low-pass band extending to approximately 40% of the sampling fre- 

 quency the basic noise power is related to the power of a sine wave signal by 



Signal power -^ , peak-to-peak signal voltage , _ ,, 



-^^ = 20 logio ^ ^ — -f 3 db 



JNoise power step voltage 



This band of noise has an amplitude distribution somewhat different from 

 thermal noise, and a spectral distribution which depends somewhat upon the 

 spectral distribution of the signal and upon its amplitude and disposition 

 with respect to the step boundaries. 



For a sine wave signal the noise spectrum is characterized by a number of 

 prominent components rising above a diffuse background of numerous 

 smaller components. The outstanding components may be either harmonics 

 of the signal frequency or dilTerences between harmonics of the sampling 

 frequency and harmonics of the signal frequency. The background thus 

 consists of an array of various orders of cross-products between the signal 

 and the sampling rate. When the amplitude of the signal is comparable to 

 one step in the quantizing process, a few components may contain a substan- 



